US 62 was commissioned in 1930. At first it went only as far east as Maysville KY (you can read more on that page).

At the time, the west end of US 62 was in Carlsbad NM - an odd terminus, considering
that there was no north-south US route serving town back then. Maybe the road
west to El Paso wasn't yet in good enough condition to include in the system.
At any rate, the photo below is looking south on Canal Street:

Elbert,
Mar. 2007 (still there as of 2010)

That's really, um... creative, the way they overlapped those signs. To the left on Greene Street may have been the original west beginning of US 62. Interestingly, from this point to the Texas state line, New Mexico signs US 62-180 as a north-south route. The shot below was taken right at the Texas line...

me,
Mar. 2010

...but the entire route between here and Carlsbad is consistently signed as north-south. Just ahead, Texas immediately changes signage back to east-west. (Incidentally, the mountain just to the left of the US 62 sign is Guadalupe Peak, which is the highest elevation in Texas. Just left of there, the mountain with the rock cliff is El Capitan - that's all part of Guadalupe Mountains National Park.) The shot
below is back in Carlsbad, from the opposite direction (north on Canal):

Elbert, Mar. 2007 (both still there as of 2010)

Old signs juxtaposed with new signs - this is where the north-south signs change back to east-west. If nothing else, the upcoming intersection
is the modern equivalent of the historic junction. Today eastbound US 62/180
continues to the right. US 285 didn't come through Carlsbad
until 1936, but before that, this segment was NM hwy. 2. So in the early 1930s,
the west beginning of US 62 was probably to the right... that is, assuming highway
traffic was always routed down Canal Street. Seems to me it may have originally
used Main Street, in which case US 62 would've begun two blocks to the right.
If we turn that way, we see the assembly below:

Elbert, Mar. 2007

The actual beginning of US 62 may have been at Main (the stoplight in the distance).
Turning around, we see this on westbound Greene at Canal:

Elbert,
Mar. 2007

That may have been the original west end of US 62. Now, it continues west (along
with US 180) by turning left, joining with southbound US 285 for about two miles.
Not far that direction, here's how that multiplex is signed:

Elbert,
Mar. 2007 (still there as of 2010)

And, heading northbound, we have this doozy:

me,
Mar. 2010

Nice, aren't they? I'm not going to add anything to what I've already said about
signage in New Mexico...

Two years later, both ends of US 62 were extended, to the same destinations
that the highway still serves today. The west terminus of US 62 is in El
Paso TX. Its endpoint there has shifted around over the years - you
can view photos and get more info on this
page.

The east end of US 62 is now at the Ohio line at Sharon PA;
the highway is signed north/south in Pennsylvania and New York. So
the Niagara Falls terminus of US 62 is actually its north end.
US 62 is routed north out of Buffalo on Niagara Falls Blvd. By the
time that road reaches Niagara, it's heading pretty much due west.
About two miles before its north end, US 62 originally followed what is now Business 62, or Pine Avenue. A 1949 USGS topo map indicates the route ended at its junction with Main Street, which carried US 104 at the time (now NY hwy. 104):

Google Maps Street View,
2011

That sign's a little messed up: what it means is, this is the end of Business 62, at its junction with NY 104. Signage at the actual intersection is shown on the left side of the photo below...

Google Maps Street View,
2011

...while on the right side is the sign for traffic heading south on Main. To the left on Pine was the original north beginning of US 62. The 1965 and 1980 topos indicate that US 62 extended ahead, co-signed with US 104 to a common terminus (for photos from there, please see my US 104 page). The shot below was taken from the opposite direction (north on Main):

Google Maps Street View,
2011

That was either the north beginning of US 62, or else the point where US 62 split off from US 104 after a brief duplex. In the 1960s, the two blocks to the south of Pine (Walnut Avenue and Ferry Avenue) were extended east to intersect Pine/US 62, and in the 1970s US 62 traffic was rerouted to follow these one-way roads. (Pine was re-designated as NY hwy. 62A, and then in 2006 it was changed to Business US 62.) Here is the final northbound sign:

Karner, June 2013

That's posted on Walnut at 7th Street. About two blocks ahead we reach the north end, which is at the
intersection with Main:

Nitzman, 2000 (same as of July 2006, but changed by 2013)

That "US 62A" sign was a mistake: at the time
it should've been NY 62A. But now it's been changed to Business US 62, so what does the sign say?...

Karner, June 2013

...NY 62. Kind of funny. But I digress: at least there's an "End" sign at US 62's northern terminus.

The shot below is looking north on
Main (or east on NY 104). To the right is eastbound Ferry Street,
which is the north beginning of US 62:

Nitzman, 2000 (unchanged as of July 2006; "Seaway Trail" signage gone by 2013)

The traffic light in the
background is Walnut, the north end of US 62. If you take that right turn onto
Ferry, you'll soon see the first southbound US 62 marker:

Morrison, Aug. 2002 (unchanged as of July 2006)

Here's a photo from southbound Main:

Elbert,
July 2006

There, signs don't direct you all the way to Ferry Street. Instead, that left
turn takes you south on 3rd Street, and then at the Ferry intersection you encounter
the sign shown below:

Elbert,
July 2006

Of course that's actually US 62 (not NY 62), but that appears to be a common problem with signs in this area.